Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On efficient sparse integer matrix Smith normal form computations
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Computation of homology groups and generators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Simplicial perturbation techniques and effective homology
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
A tool for integer homology computation: λ-AT-model
Image and Vision Computing
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
Using Membrane Computing for Obtaining Homology Groups of Binary 2D Digital Images
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
A graph-with-loop structure for a topological representation of 3D objects
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
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When the ground ring is a field, the notion of algebraic topological model (AT-model) is a useful tool for computing (co)homology, representative (co)cycles of (co)homology generators and the cup product on cohomology of nD digital images as well as for controlling topological information when the image suffers local changes [6,7,9]. In this paper, we formalize the notion of λ-AT-model (λ being an integer) which extends the one of AT-model and allows the computation of homological information in the integer domain without computing the Smith Normal Form of the boundary matrices. We present an algorithm for computing such a model, obtaining Betti numbers, the prime numbers p involved in the invariant factors (corresponding to the torsion subgroup of the homology), the amount of invariant factors that are a power of p and a set of representative cycles of the generators of homology mod p, for such p.